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<p>In the circular restricted three-body problem (CRTBP), periodic orbits in the vicinity of collinear libration points not only exhibit profound nonlinear dynamical characteristics but also serve as critical orbital resources for deep-space exploration mission design. In this study, we introduce a systematic analytical framework based on the Homotopy Analysis Method (HAM) to construct high-order series solutions for Lyapunov and Halo orbits near the libration points. The convergence behavior of the series solutions is thoroughly investigated, and their accuracy is validated through comparison with high-precision numerical integration results. The results indicate that the HAM-based solutions exhibit good agreement with the numerical results. Consequently, the initial conditions derived from the HAM series solutions provide enhanced accuracy and reliability for the practical computation of periodic orbits in mission design and trajectory analysis.</p>

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Series solution of periodic orbits around collinear libration point in the circular restricted three-body problem by homotopy analysis method

  • 期刊论文

  • 发表日期：

    2026年5月18日

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  • Zhe Dong,
  • Xiaochen Li,
  • Jifeng Cui,
  • Xiaoming Li

摘要

In the circular restricted three-body problem (CRTBP), periodic orbits in the vicinity of collinear libration points not only exhibit profound nonlinear dynamical characteristics but also serve as critical orbital resources for deep-space exploration mission design. In this study, we introduce a systematic analytical framework based on the Homotopy Analysis Method (HAM) to construct high-order series solutions for Lyapunov and Halo orbits near the libration points. The convergence behavior of the series solutions is thoroughly investigated, and their accuracy is validated through comparison with high-precision numerical integration results. The results indicate that the HAM-based solutions exhibit good agreement with the numerical results. Consequently, the initial conditions derived from the HAM series solutions provide enhanced accuracy and reliability for the practical computation of periodic orbits in mission design and trajectory analysis.